How do I get rid of curved edges that bridge the two edge loops together in attached model below?
Reasons:


The edge is missing a crease, so the Subdivision Modifier deforms it.
You've enabled the On Cage option in the modifier panel, which prevents you from noticing it.
Your model is too low poly, the Subdivision modifier doesn't know which way to curve the edges.


Solution  


Add a crease to the edge, or add some loopcuts.
Disable the On Cage option - it has no benefit here, only hides real geometry.
Add more geometry, so you can better control the curvature.




Add more geometry.
If you only add loopcuts, you'll need to correct the shape.
It's easier to rebuild the model with more sides.